Question

Finitely generated abelian groups $G,H$ with the same finite quotients (up to isomorphism) are isomorphic

score 63 · Answer 1 · 2026-03-26 21:09:14

63

Views

Finitely generated abelian groups $G,H$ with the same finite quotients (up to isomorphism) are isomorphic

Published on 26 Mar 2026 - 21:09

score 147 · Answer 2 · 2023-02-09 02:37:21

147

Views

Is $PGL(2,\mathbb R)$ isomorphic to $SO(1,2)$?

Published on 09 Feb 2023 - 2:37

score 92 · Answer 3 · 2026-03-31 22:24:48

92

Views

Generalized Zassenhaus Lemma

Published on 31 Mar 2026 - 22:24

score 28 · Answer 4 · 2026-03-30 02:06:37

28

Views

Show that $SL(2,\mathbb{Z}) / \Gamma (n)$ is isomorphic to $SL(2,\mathbb{Z}_n)$.

Published on 30 Mar 2026 - 2:06

score 54 · Answer 5 · 2026-03-26 21:14:00

54

Views

When do $H_1 \cong H_2$ and $K_1 \cong K_2$ imply $F(H_1,K_1) \cong F(H_2,K_2)$?

Published on 26 Mar 2026 - 21:14

score 90 · Answer 6 · 2026-03-27 00:58:10

90

Views

Prove $D_6 \cdot \text{stab}_{S6}(2) \leq S_6.$

Published on 27 Mar 2026 - 0:58

score 98 · Answer 7 · 2026-03-26 10:58:23

98

Views

Does $[G:H]=|G/H|$ hold for infinite groups?

Published on 26 Mar 2026 - 10:58

score 128 · Answer 8 · 2023-02-25 02:05:01

128

Views

Is the character group of the character group of G isomorphic to G?

Published on 25 Feb 2023 - 2:05

score 82 · Answer 9 · 2026-03-25 20:17:37

82

Views

Group Isomorphism from $\mathbb{Q}[X]^2$ to $\mathbb{Q}[X]$.

Published on 25 Mar 2026 - 20:17

score 464 · Answer 10 · 2026-03-27 12:27:29

464

Views

Proof of Chinese remainder theorem by isomorphism

Published on 27 Mar 2026 - 12:27

score 27 · Answer 11 · 2026-03-26 14:23:02

27

Views

A monoid structure $$ on all of $\Bbb{Z}$ isomorphic to $A \Bbb{Z} + 1$ for some $A \neq 0,1$ is such that $\Bbb{Z}\Bbb{Z}$ has infinite complement.

Published on 26 Mar 2026 - 14:23

score 155 · Answer 12 · 2026-03-29 21:58:15

155

Views

Graph Theory - Bondy & Murty exercise 1.2.15

Published on 29 Mar 2026 - 21:58

score 90 · Answer 13 · 2026-03-27 02:34:10

90

Views

Help understanding how to show that two groups are isomorphic

Published on 27 Mar 2026 - 2:34

score 97 · Answer 14 · 2026-03-31 22:29:23

97

Views

$K \unlhd A \rightarrow \Phi(A)$ is isomorphism

Published on 31 Mar 2026 - 22:29

score 153 · Answer 15 · 2023-03-18 05:06:46

153

Views

$\phi:G\to \bar G$ is an isomorphism. Then the equation $x^k=b$ has the same number of solutions in $G$ as the equation $x^k=\phi(b)$ in $\bar G$

Published on 18 Mar 2023 - 5:06

List Question

Finitely generated abelian groups $G,H$ with the same finite quotients (up to isomorphism) are isomorphic

Is $PGL(2,\mathbb R)$ isomorphic to $SO(1,2)$?

Generalized Zassenhaus Lemma

Show that $SL(2,\mathbb{Z}) / \Gamma (n)$ is isomorphic to $SL(2,\mathbb{Z}_n)$.

When do $H_1 \cong H_2$ and $K_1 \cong K_2$ imply $F(H_1,K_1) \cong F(H_2,K_2)$?

Prove $D_6 \cdot \text{stab}_{S6}(2) \leq S_6.$

Does $[G:H]=|G/H|$ hold for infinite groups?

Is the character group of the character group of G isomorphic to G?

Group Isomorphism from $\mathbb{Q}[X]^2$ to $\mathbb{Q}[X]$.

Proof of Chinese remainder theorem by isomorphism

A monoid structure $$ on all of $\Bbb{Z}$ isomorphic to $A \Bbb{Z} + 1$ for some $A \neq 0,1$ is such that $\Bbb{Z}\Bbb{Z}$ has infinite complement.

Graph Theory - Bondy & Murty exercise 1.2.15

Help understanding how to show that two groups are isomorphic

$K \unlhd A \rightarrow \Phi(A)$ is isomorphism

$\phi:G\to \bar G$ is an isomorphism. Then the equation $x^k=b$ has the same number of solutions in $G$ as the equation $x^k=\phi(b)$ in $\bar G$

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